When a customer order is received at a facility such as distribution center, assembly center, or any other business that may receive orders, there are several ways of fulfilling the order. One method is to fulfill directly from the inventory of products or components or like, provided that sufficient inventory exists. In situations where there is not enough inventory to fulfill the order at the site that receives the order, the supply of items has to be shipped from another location, typically the supplier, to the fulfillment facility. For this situation, there can be more than one way of transporting the supply from the supplier to the fulfillment center (for example, distribution center). For instance, the goods may be shipped by premium air, ocean transportation, ground transportation, etc. Shipping by premium air may be faster than other methods but costs more, and shipping by ocean transportation costs much less than premium air, but takes substantially longer.
Thus, the following are some example ways for handling incoming orders: fulfill directly from the on-hand inventory of product or components (no lead time); fulfill from in-transit inventory (some lead time depending on where the shipment is); order a shipment from a supplier via fast transportation mode such as premium air transportation (short lead time, for example, 3-5 days, but with substantially high transportation cost); order a shipment from a supplier via slower transportation mode such as ocean freight (long lead time, for example, 5 weeks, however, less costly than premium air shipment).
The decision on which fulfillment alternatives to use depends on many factors such as requested ship date, service level agreement (SLA) for various customers, realized order/demand forecast, order backlog, customer and/or order priority, transportation costs, budget for transportation expense, and inventory levels or positions in the supply pipeline, that is, inventory on-hand, in-transit or on-order. To efficiently and profitably fulfill the orders, an optimal decision that considers and balances many factors need to be made. However, current methodologies do not provide practical and useful solution to the problem. For instance, standard inventory policies such as reorder point policy, which determines when to place an order for replenishing current inventory, and (s, S) policy, where s represents the inventory position which triggers re-ordering, and S represents target inventory which should be reached as a result of the re-ordering, do not consider multiple transportation modes. In general, no existing decision support system makes inventory replenishment decision and transportation decision jointly by minimizing the overall cost of both decisions. No standard industry practice is reported for joint inventory and transportation decision. Rather, the fulfillment decision is typically made by simple ad-hoc, business rules.
Recent research described in Sethi, Yan, and Zhang, “Peeling Layers of an Onion: Periodic Review Inventory Model with Multiple Delivery Modes and Forecast Updates,” Journal of Optimization Theory and Applications, Vol. 108, pp. 253-281, 2001 (“Sethi et al.”); Zhang, “Ordering policies for an inventory system with three supply modes,” Naval Research Logistics, Vol. 43, No. 5, pp. 691-708, 1996 (“Zhang”); and Scheller-Wolf and Tayur, “A Markovian Dual-Source Production-Inventory Model with Order Bands,” GSIA Working Paper No. 1998-E200, Carnegie Mellon University, 1998 (“Scheller-Wolf et al.”), extended the standard model in the literature by allowing multiple delivery modes. However, the solution methods proposed in Sethi et al. and Zhang are based on periodic planning models with assumptions that the transportation lead times must be consecutive. The decision rules derived from the existing methods typically deal with stationary demand only. They do not take into account the different demand priorities of orders. Furthermore, inventory decisions in Scheller-Wolf et al. are made based on the inventory position only without analyzing the pipeline inventory information at each stage of the supply chain.